Variations in the fractal dimension of fluctuations of the ionospheric <Emphasis Type="Italic">F</Emphasis>2 layer critical frequency

The 40-year period of observations of short-term variations (with characteristic times of up to 1–2 days) in the critical frequency of the ionospheric F2 layer (foF2) is analyzed. The continuous (with a step of 1 h) series of fluctuations (F) of the foF2 critical frequency (with eliminated daily variations) has been calculated using the hourly variations in foF2 at Moscow stations. The fractal dimension (FRH) of the fluctuations, characterizing short-term variations in foF2, has been determined and analyzed on a 30-day interval, using the Higuchi method. It has been established that FRH estimates substantially change in time. The 11-year cycle, which is in antiphase with the solar cycle, and the total annual and semiannual variations, similar to the variations observed in the normalized critical frequency of the E region and in the electron density of the D region, are clearly defined in these changes. Thus, the parameters of fast variations in the ionospheric F2 layer are affected by the phase of the 11-year solar cycle and by the position of the Earth in the orbit or seasonal variations in the atmosphere.     

Properties of the <Emphasis Type="Italic">F</Emphasis>2-layer critical frequency median in the nocturnal subauroral ionosphere during low and moderate solar activity

Based on an analysis of data from the European ionospheric stations at subauroral latitudes, it has been found that the main ionospheric trough (MIT) is not characteristic for the monthly median of the F2-layer critical frequency (foF2), at least for low and moderate solar activity. In order to explain this effect, the properties of foF2 in the nocturnal subauroral ionosphere have been additionally studied for low geomagnetic activity, when the MIT localization is known quite reliably. It has been found that at low and moderate solar activity during night hours in winter, the foF2 data from ionospheric stations are often absent in the MIT area. For this reason, a model of the foF2 monthly median, which was constructed from the remaining data of these stations, contains no MIT or a very weakly pronounced MIT.     

Global empirical model of critical frequency of the ionospheric <Emphasis Type="Italic">F</Emphasis>2-layer for quiet geomagnetic conditions

Using the foF2 database obtained from satellites and ground-based ionospheric stations, we have constructed a global empirical model of the critical frequency of the ionospheric F2-layer (SDMF2—Satellite and Digisonde Data Model of the F2 layer) for quiet geomagnetic conditions (Kp < 3). The input parameters of this model are the geographical coordinates, UT, day, month, year, and the integral index F10.7 (day, τ = 0.96) of solar activity for a given day. The SDMF2 model was based on the Legendre method for the spatial expansion of foF2 monthly medians to 12 in latitude and 8 in longitude of spherical harmonics. The resulting spatial coefficients have been expanded by the Fourier method in three spherical harmonics with respect to UT. The effect of the saturation of critical frequency of the ionospheric F2-layer at high solar activity was described in the SDMF2 model by foF2 as a logarithmic function of F10.7 (day, τ = 0.96). The difference between the SDMF2 and IRI models is a maximum at low solar activity as well as in the Southern Hemisphere and in the oceans. The testing on the basis of ground-based and satellite data has indicated that the SDMF2 model is more accurate than the IRI model.     

Increase in the critical frequency of the ionospheric <Emphasis Type="Italic">F</Emphasis> region prior to the substorm expansion phase

Specific variations in the critical frequency of the ionospheric F ₂ layer during magnetospheric substorms have been found based on the data of vertical sounding stations in Europe and North America. Maximal attention has been paid to the positive peaks of ΔfoF2 with a duration of 6–8 h before the beginning of the substorm expansion phase (T ₀). The possible physical mechanisms by which these peaks are formed (related to the impact of fast particles in the foreshock region of the solar wind on the Earth’s magnetosphere and different for middle and high latitudes) have been considered. The positive peaks of ΔfoF2 can be used in a short-term prediction of the ionospheric disturbance onset and space weather on the whole.     

Statistical Analysis and Modeling of the Local Ionospheric Critical Frequency: A Mid-latitude Single-Station Model for Use in Forecasting

The hourly values of the F-layer critical frequency from the ionospheric sounder in Dourbes (50.1°N, 4.6°E) during the time interval from 1957 to 2010, comprising five solar cycles, were analyzed for the effects of the solar activity. The hourly time series were reduced to hourly monthly medians which in turn were used for fitting a single station foF₂ monthly median model. Two functional approaches have been investigated: a statistical approach and a spectral approach. The solar flux F_10.7 is used to model the dependence of foF₂ on the solar activity and is incorporated into both models by a polynomial expression. The statistical model employs polynomial functions to fit the F-layer critical frequency while the spectral model is based on spectral decomposition of the measured data and offers a better physical interpretation of the fitting parameters. The daytime and nighttime foF₂ values calculated by both approaches are compared during high and low solar activity. In general, the statistical model has a slightly lower uncertainty at the expense of the larger number of fitting parameters. However, the spectral approach is superior for modeling the periodic effects and performs better when comparing the results for high and low solar activity. Comparison with the International Reference Ionosphere (IRI 2012) shows that both local models are better at describing the local values of the F-layer critical frequency.     

Observations of large-scale plasma convection in the magnetosphere with respect to the geomagnetic activity level

The data of the ionospheric observations (the daily f plots) at the Yakutsk meridional chain of ionosondes (Yakutsk–Zhigansk–Batagai–Tixie Bay) with sharp decreases (breaks) in the critical frequency of the regular ionospheric F2 layer (foF2) are considered. The data for 1968–1983 were analyzed, and the statistics of the foF2 break observations, which indicate that these breaks are mainly registered in equinoctial months and in afternoon and evening hours under moderately disturbed geomagnetic conditions, are presented. Calculations performed using the prognostic model of the high-latitude ionosphere indicate that the critical frequency break position coincides with the equatorial boundary of large-scale plasma convection in the dusk MLT sector.     

Long-term trends in the ratio of the daytime and nighttime values of <Emphasis Type="Italic">foF</Emphasis>2

The consideration of the relation between the daytime and nighttime values of the critical frequency F2, foF2 of the ionospheric F2 layer, started in the previous publication of the authors, is continued. The main regularities in variations in the correlation coefficient R(foF2) characterizing this relation are confirmed using larger statistical material (more ionospheric stations and longer observational series). Long-term trends in the R(foF2) value are found: at all stations the negative value of R(foF2) increases with time after 1980.     

Properties of solar activity and ionosphere for solar cycle 25

Based on the known forecast of solar cycle 25 amplitude (Rz _max ≈ 50), the first assessments of the shape and amplitude of this cycle in the index of solar activity F10.7 (the magnitude of solar radio flux at the 10.7 cm wavelength) are given. It has been found that (F10.7)_max ≈ 115, which means that it is the lowest solar cycle ever encountered in the history of regular ionospheric measurements. For this reason, many ionospheric parameters for cycle 25, including the F2-layer peak height and critical frequency (hmF2 and foF2), will be extremely low. For example, at middle latitudes, typical foF2 values will not exceed 8–10 MHz, which makes ionospheric heating ineffective in the area of upper hybrid resonance at frequencies higher than 10 MHz. The density of the atmosphere will also be extremely low, which significantly extends the lifetime of low-orbit satellites. The probability of F-spread will be increased, especially during night hours.     

Comparison of Ionospheric Parameters during Similar Geomagnetic Storms

The degree of closeness of ionospheric parameters during one magnetic storm and of the same parameters during another, similar, storm is estimated. Overall, four storms—two pairs of storms close in structure and appearance according to recording of the magnetic field Х-component—were analyzed. The examination was based on data from Sodankyla observatory (Finland). The f-graphs of the ionospheric vertical sounding, magnetometer data, and riometer data on absorption were used. The main results are as follows. The values of the critical frequencies foF2, foF1, and foE for different but similar magnetic storms differ insignificantly. In the daytime, the difference is on average 6% (from 0 to 11.1%) for all ionospheric layers. In the nighttime conditions, the difference for foF2 is 4%. The nighttime values of foEs differ on average by 20%. These estimates potentially make it possible to forecast ionospheric parameters for a particular storm.     

Geomagnetic activity that corresponds to the median of the <Emphasis Type="Italic">F</Emphasis>2-layer critical frequency at various latitudes

On the basis of the F2-layer critical frequency foF2 for the noon at some European stations for 1958–2005, it is found that the geomagnetic activity corresponding to the foF2 median is systematically lower than that averaged over the month; the difference increases with an increase in latitude. Moreover, the dispersion of geomagnetic activity for the foF2 median at relatively high latitudes is lower than at middle latitudes. These regularities are related to the fact that high geomagnetic activity usually leads to a distinct deviation of foF2 from the typical average value, i.e., from the foF2 median, and such deviation is more substantial at relatively high latitudes. That is why the geomagnetic activity for the foF2 median is lower at relatively high latitudes than at middle latitudes.     

Spatial inhomogeneity of variations in the <Emphasis Type="Italic">F</Emphasis><Subscript>2</Subscript> layer critical frequencies under the conditions of winter 1995

The daily samples of the hourly measurements of the foF2 critical frequency, obtained on January 5–21, 1995, at the midlatitude and high-latitude automated ionospheric stations (geographic latitude higher than 60°), are considered. The {fo} sets are transformed into the {δfoF2} sets of relative variations, for which asymmetry (A) and excess (E) are calculated. The selected stations are grouped into 20 pairs of automated ionospheric stations (AISs) located at distances of 200–10 000 km from one another. Sign estimates of the cross-correlation coefficients between the sets of 16 A and E values for different pairs of stations are used. Two types of structures of the statistical invariant spatial distribution are established: the structures with a scale of about 300 km, invariant with respect to latitude, and with a scale of about 6000 km (for only high latitudes).     

Ionosphere Disturbances Preceding Earthquakes according to the Data of Ground Based Station of the Vertical Ionospheric Sounding Wakkanai

The paper analyzes the data of manual ionograms processing of hourly measurements of the critical frequency foF2 of the F2 ionospheric layer at the Wakkanai ionospheric vertical sounding station (Japan) in a geomagnetically quiet environment before a series of earthquakes with magnitude M > 6.0, for which the station entered the earthquake preparation zone, in order to detect possible Ionospheric Disturbances Preceding Earthquakes (IDPE), and to determine their quantitative characteristics. Detected IDPE, in the opinion of the authors, can be related to the processes of preparation of the corresponding earthquakes, i.e., to be Ionospheric Precursors of Earthquakes (IPE).     

Regular changes in the critical frequency of the <Emphasis Type="Italic">F</Emphasis>2 layer of the quiet midlatitude ionosphere

A method for constructing the empirical model of the F2 layer critical frequency (foF2) under magnetically quiet conditions, aimed at analyzing disturbances of any nature, is proposed. This method has been analyzed, and typical features of regular changes in foF2 of the quiet ionosphere and day-to-day foF2 variability are analyzed using the data from Irkutsk and Slough stations as an example. In particular, it has been obtained that this model differs from the international IRI model, and this difference is mainly caused by the fact that the foF2 values in the IRI model do not correspond to quiet conditions. Therefore, this model gives a larger amplitude of the annual and semiannual variations in foF2 than the IRI model. In addition, this model more accurately reproduces the rate of foF2 annual variations at a fixed local time, especially in equinoxes, when foF2 variations can exceed 1 MHz within one month.     

Long-term changes in the Delta <Emphasis Type="Italic">foF</Emphasis>2 parameter based on the data of two European ionospheric stations

Analysis of changes in the critical frequency foF2 in recent decades has been performed by determination of “Delta foF2” parameter. These values determine the mean change of foF2 values from the “etalon period” (1958–1980) to later periods. The results are compared with the determination of foF2 trends, which was performed in a series of previous publications of the authors. The data of two most reliable ionospheric stations of the European region, Slough and Juliusruh, are analyzed. The results confirm all principal conclusions obtained earlier, which were based on analysis of the trends. A systematic decrease of foF2 with time occurs (which corresponds to a negative trend), and the character of changes in the Delta values with season and local time on the whole agrees with the character of changes in the trend. It is shown that the results based on the data of both considered stations show good agreement.     

Quasibiennial variations in fractal dimension of solar total irradiance

Based on the Nimbus-7 (1978–1992) data and the parameters of solar activity (Wolf numbers W, solar radioemission F _10.7) and the ionosphere (f ₂ index of the critical frequency of the ionospheric F ₂ layer normalized to noon), the fractal dimension (FD) of the variations in the solar total irradiance (L) has been determined on the moving annual interval using the Higuchi technique. It has been established that FD estimates substantially vary in time. Quasibiennial variations (QBVs), which similarly manifest themselves in all considered processes, are detected in these variations. It is interesting that all fractal QBVs are in phase with QBVs of solar irradiance (L) and are almost in antiphase with QBVs of initial (filtered) W, F _10.7, and f ₂ indices. The presence of QBVs in the solar processes and in their FD and noncoincidence of the former with the latter in phase indicate that QBVs have a two-component structure. The obtained results also indicate that an analysis of the annual FD estimates of the solar and ionospheric processes in studying variations in these processes is reliable.     

Relation of long-period variations in the critical frequencies of the <Emphasis Type="Italic">F</Emphasis><Subscript>2</Subscript> layer to geomagnetic activity

The relation of the long-period variations in the midnight and noon values of the critical frequency of the ionospheric F ₂ layer at three midlatitude stations (Irkutsk, Moscow, and Boulder) to the daily mean index of geomagnetic activity in years of different solar activity has been studied. It has been found that the correlation coefficients between the above parameters depend on time of day, season, and solar activity level. The correlation coefficients are higher at night than in the daytime, especially at low solar activity. The highest absolute values of the correlation coefficient most often appear during equinoxes: April–May and September–October. It has been shown that the variability of the critical frequencies of the midlatitude ionospheric F ₂ layer depends not only on geomagnetic activity but also (to a considerable degree) on the effect of the lower atmosphere.     

Critical frequencies <Emphasis Type="Italic">foF</Emphasis>2 as an indicator of trends in thermospheric dynamics

The time variations in three parameters during the last decades are considered. R(foF2) is the correlation coefficient between the nighttime and daytime values of foF2 for the same day. Stable trends are found for the minimum (R(foF2)(max)) and maximum (R(foF2)(min)) values of R(foF2) during a year. The foF2(night)/foF2(day) ratio demonstrates both, negative and positive trends, and the trend sign depends on the inclination I and declination D of the magnetic field. The correlation coefficient r(h, fo) between foF2 and the 100 hP level in the stratosphere demonstrates a decrease (in the years of maximum and minimum solar activity) from the 1980s to the 1990s. The trends in all three groups of data are considered under the assumption of long-term changes in the circulation in the upper atmosphere.